Sojourn time of almost semicontinuous integral-valued processes in a fixed state

• Date: 2011
• Main Authors: Gusak, D. V., Гусак, Д. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2782
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $\xi(t)$ be an almost lower semicontinuous integer-valued process with the moment generating function of the negative part of jumps $\xi_k : \textbf{E}[z^{\xi_k} / \xi_k < 0] = \frac{1 − b}{z − b},\quad 0 ≤ b < 1.$ For the moment generating function of the sojourn time of $\xi(...